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The Multidimensional Darboux transformation

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González López, Artemio and Kamran, Niky (1998) The Multidimensional Darboux transformation. Journal of geometry and physics, 26 (3-abr.). pp. 202-226. ISSN 0393-0440

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Official URL: http://dx.doi.org/10.1016/S0393-0440(97)00044-2




Abstract

A generalization of the classical one-dimensional Darboux transformation to arbitrary n- dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n ≥ 2. New examples of quasi-exactly solvable multidimensional matrix Schrödinger operators on curved manifolds are obtained by applying the above results.


Item Type:Article
Additional Information:

© Elsevier.
One of the authors (A.G.-L.) would like to thank A. Galindo, M. Mañas and M. A. Martín Delgado for helpful conversations.

Uncontrolled Keywords:Quantum-systems; Supersymmetry; Dimensions
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32861
Deposited On:25 Aug 2015 09:37
Last Modified:10 Dec 2018 15:10

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